Often the simple answer is that depends on the "tradition" of the code.

Then, "better" is too general. We should focus on accuracy and computational cost and hence on the resulting efficiency. FEM is somehow less efficient than FVM for higly non-linear flows but recently DG method received new attention in the CFD community.

Finally, I would stress that FVM is nothing else that a FEM for a specific choice of the test-function.

Dear Steffen, FEM is born in the context of Structural Analysis, while FVM in the context of Fluid Dynamics. From a theoretical point of view, FVM should better of FEM for CFD because continuity of mass is "native" in FVM.

COMSOL is born from original Matlab PDE Toolbox, which used FEM for solving PDE 2D problems; I think that Comsol uses FEM in CFD for compatibility with original numerical algorithms.

Gianluca

FVM is generally better than FEM. Reasons: FEM does volumeric integral and not are exactly conservative. However, FVM does surface integrals and is exactly conservative. In Openfoam, FVM is mainly used. So, this is what I learned from a seminar in my university.

Often the simple answer is that depends on the "tradition" of the code.

Then, "better" is too general. We should focus on accuracy and computational cost and hence on the resulting efficiency. FEM is somehow less efficient than FVM for higly non-linear flows but recently DG method received new attention in the CFD community.

Finally, I would stress that FVM is nothing else that a FEM for a specific choice of the test-function.

In general, commercial and in-house CFD codes are based on the FVM (comparing only FVM and FEM). There are few exceptions regarding to FEM - few CFD codes using FEM - most of all due to the complexity of the code and conservation issues.

I belive that FVM is more suitable for CFD (from a theoretical point of view both cam be used, just like theoretically FDM can be used for CFD in complex geometries)

As many people have commented, FEM is mostly suitable and used for structural analysis. Many times CFD analysis is carried out in the flow domain whose output is used as boundary condition for FEM analysis. However, FEM analysis output is hardly used for CFD, but geometrical change due to structural loading or deflection will affect the flow pattern. This greatly depends on material and geometry / pattern of the object under investigation. In your case, what is the type of object and analysis you are looking for?

I ask this question for my Curiosity (as i know both FEM and FVM).

I want to know that why COMSOL use FEM...

FEM methods in CFD problems is, among others, an attempt to deal with numerical diffusion. Certainly within acoustics or other wave propagation problems this would be beneficial. With FVM you cannot do better than 2nd order discretisation but with FEM you can get higher. It might also be easier to couple it to other physical problems like fluid structure interaction, heat problems or electrical/magnetic problems. But for that you get other numerical problems in return. I must say I'm not fully up to date with these kind of solvers.

In Comsol there is more compatibility with the Cad files and better Meshing and quick convergence. I compared the results with the Other studies, It was accurate.

FVM performs better than FEM in terms of accuracy, but the cost of computation is more.

Finite Difference, Volume and Element Methods are all used to approximate the solution using numerical methods. None of these provide accurate solutions. The difference between the three are the mathematical model/governing equations used for computation. Depending on the precision of solution you want, you may use either of three. FDM provides the least acceptable approximate for minimal computation cost while FVM provides best approximate with high computational cost.FEM is used by most simulators as it provides acceptable approximation with lower computations than Finite Volume.

To learn more, you may look at the differential equations used in the three methods.

Its depend on ur computer hardware and turbulence you chose. for example DNS can reach accurate solutions.

Source:

https://www.cfd-online.com/Forums/main/197380-why-comsol-use-fem-instead-fvm.html

FEM lacks a fundamental statement of conservation. FVM (and DG) are axiomatically conservative based on face flux integrals. FEM is defined as a minimization problem--find the solution that best reduces the Galerkin (or Least-Squares) residual of this system. For solid mechanics, that minimization statement makes a lot of sense--configuration of solid mechanical systems map nicely to variational formulations. Conservation equations, however, do not.

For simple flow physics, the difference is not really that important. FEM with linear shape functions *may* be a little more accurate than 2nd order FVM on a per-DOF basis. The FVM code will probably run a bit faster. But, the FVM code will *precisely* (to round-off error) conserve the mass entering and exiting a system. FEM will not be absolutely conservative, without some additional tweaking--using dark arts that I know not. This really becomes an issue with reacting flows, say, where trace concentrations of species can make significant differences. A one-part-in-ten-thousand mass imbalance is inconsequential in external aero or a lid driven cavity, but it could create a dramatic difference in flame shape or attachment points.

Another reason is that FVM solvers are highly optimised for solving flow problems, by basically cutting every corner possible. Segregated solution methods, projection methods, frozen field preconditioning for Newton Krystal...the list is very long. FEM doesn't have these and they do not automatically transfer. FEM tends to do a great job of handling inter-field coupling because it creates a large stiffness matrix using all of the d.o.f.s, solving the system in a coupled manner. And while that is perfect for enforcing solid mechanics constitutive laws, that coupled approach *tends* to be sub optimal from a pure convergence/performance standpoint. The details of these differences are difficult to cover without really getting into the weeds. Suffice to say, FEM methods have grown one way to serve primarily solid mechanics. FVM methods have grown another way (really TWO other ways, as density-based and pressure-based solvers are hugely different in their own right). These decades of accumulated differences has resulted in tool specialisation that is hard to overcome.

The advantages of FEM are dynamically observed in numerical experiments and based on the mathematical variational formulation. It is better if you read the paper :

Advection schemes for unstructured grid ocean modelling  [2006], Hanert, E.Le Roux, D.Y.Legat, V.Deleersnijder, E.

The paper shows also that any FEM option is better that FVM.

Regards

For multiphysics simulations, energy coupling is important. FEM based on energy variational formulation maybe best fit into the scope.